Question

Design a circuit that determines the magnitude of the difference D₁D₀ of two-bit numbers A₁A₀ and B₁B₀ .; i.e. D₁D₀ = |A₁A₀ - B₁B₀l. The first eight rows of the function table are provided below. The function table will have sixteen rows total.

A(1..0) B(1..0) D(1..0)
00 00 00
00 01 01
00 10 10
00 11 11
01 00 01
01 01 00
01 10 01
01 11 10

Table 1. Function Table for Magnitude, First Eight Rows

Realize the expressions for the result DiDo using only SSI NAND and NOT gates using as few gates as possible (realize the MSOP expression using a NAND-DOR circuit). Using the schematic entry feature of Quartus Il software, enter, compile, and simulate your design. Verify the correct operation of your circuit simulation, i.e. the simulation should match the function table from your design.
Determine the transistor count and worst-case circuit delay for the NAND-DOR circuit.

Answer 1

Designing a circuit to find the difference in magnitude between two 2-bit numbers includes deriving the truth table, formulating the MSOP using NAND and NOT gates, simulating the design in Quartus II, and analyzing transistor count and delay.

Step-by-step explanation:

To design a circuit that determines the magnitude of the difference D1D0 of two 2-bit numbers A1A0 and B1B0, we need to look at the provided function table which tells us the expected output for each combination of inputs. We can then derive the truth table for all 16 possible input combinations (since each number can be from 00 to 11 in binary), and from there we formulate Boolean expressions for D1 and D0. These Boolean expressions can then be simplified to get the Minimal Sum of Products (MSOP) form.

Once we have the MSOP expressions for D1 and D0, the circuit can be realized using only SSI NAND and NOT gates. In this design, a NOT operation can be realized by connecting two identical inputs to a NAND gate. To verify the circuit, we enter it into the Quartus II software and simulate to ensure the output matches the function table.

Finally, to determine the transistor count, we account for the transistors in each NAND gate and inverters, typically 4 transistors per NAND and 2 per inverter. The worst-case circuit delay can be analyzed by identifying the longest path a signal must travel through the logic gates from input to output.

Answer 2

To design a circuit determining the magnitude of the difference D₁D₀ of two-bit numbers A₁A₀ and B₁B₀, I propose using SSI NAND and NOT gates. The realization involves constructing a NAND-DOR circuit to implement the MSOP expression, minimizing the number of gates. The design is then entered, compiled, and simulated using Quartus II software to ensure its correctness by comparing the simulation results with the provided function table.

Step-by-step explanation:

The circuit design is based on the provided function table for the magnitude of the difference. Using SSI NAND and NOT gates ensures simplicity and efficiency in the design. The MSOP expression is implemented through a NAND-DOR circuit, which combines NAND gates and OR gates to achieve the desired logic. The goal is to use as few gates as possible to optimize the design while maintaining accuracy.

In Quartus II software, the schematic entry feature is utilized to input, compile, and simulate the designed circuit. Simulating the circuit is crucial for verifying its correct operation, ensuring that the output matches the expected results from the given function table. This step is essential in validating the functionality of the circuit before any physical implementation.

Additionally, determining the transistor count and worst-case circuit delay for the NAND-DOR circuit is a crucial aspect of assessing the circuit's performance. Transistor count provides insight into the complexity of the circuit, while worst-case circuit delay helps in understanding the maximum time it takes for the circuit to produce a valid output. These metrics contribute to evaluating the efficiency and reliability of the designed circuit.